From another perspective, for large-scale inventory optimization problems, the number of samples used in the optimization process is not very large, typically less than number of decision variables (i.e., the base-stock levels). Thus, it is an over-parameterized model [1]}, and the bias of the sample optimal value cannot be ignored. To reduce the bias in the optimal solution, regularization methods are also typically used [2]}. Therefore, the \(L_1\)  regularization introduced in Problem (REF ) not only keeps the inventory only at a small fraction of the nodes, it also helps reduce the bias.
